Hamlet is often described as a play about the conflict between thought (or words about thoughts) and action. Consider this idea in terms of the character and the plot. Then, consider it more deeply, in terms of the discrepancy (inconsistency) between emotion and expression: i.e., the problem of representation, through words or acts, of internal states.
In Hamlet, the main character struggles with his feelings, thoughts, and actions. Young Hamlet is torn between his desire to avenge his father's murderous death and his lack of courage to follow through. Truly, Hamlet does not act on his desire to avenge his father's death quickly enough. He hesitates due to the fact that he is not sure his Uncle Claudius has killed his father.
Hamlet's father appears as a ghost and instructs his son to avenge his death. While Hamlet wants to believe his father's ghost, he is not certain that his Uncle Claudius is truly guilty.
While Hamlet devises a plan to learn the truth about his Uncle Claudius, Hamlet remains inactive. Young Hamlet asks traveling actors to reenact the murderous scene that killed King Hamlet. During the reenactment, Hamlet's Uncle Claudius appears guilty. Claudius rises and begins to cry out for the lights to be lit:
Give me some light. Let’s go!
Clearly, King Claudius is upset. He retires to his bedchamber. He definitely acts guilty. Hamlet has the proof he needs to act on his vengeance. At this point in the play, Hamlet goes to seek his Uncle Claudius. It appears that Hamlet's hesitancy is over. It appears that Hamlet will kill Claudius and get revenge.
When Hamlet finds Claudius, he is praying, asking for forgiveness of his sins. This causes Hamlet to hesitate once again. Again, Hamlet is hesitant in avenging his father's death. He does not want to kill Claudius while he is praying. He does not want Claudius to find redemption. Hamlet desires for Claudius to go to hell rather than heaven:
Now might I do it just like that, now that he is praying,
And now I’ll do it, and so he goes to heaven,
And so am I revenged. I must think about that.
A villain kills my father, and for that,
I, his sole son, do this same villain send
Hamlet decides to postpone killing his Uncle Claudius. Hamlet says "no" to killing Claudius right now:
To take him in the cleansing of his soul,
When he is fit and ready for his death?
Internally, Hamlet is in turmoil. He is struggling with the decision to kill Claudius or not. Hamlet reveals his inner conflict in his most famous soliloquy. Hamlet questions whether he should kill Claudius or continue to suffer in his mind:
To be, or not to be, that is the question.
Is it nobler in the mind to suffer
The slings and arrows of outrageous fortune
Or to fight against a sea of troubles,
And end them by fighting?
No doubt, Hamlet will not rest until he kills Claudius.